Consider a 1D finite potential well with a well width (a) of 2nm and a well...

    

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Consider a 1D finite potential well with a well width (a) of 2nm and a well depth (Vo) of 3 eV. E V₂ =3 ev a = 2 nm a. The infinite space can be approximated by periodic lattices. Assuming a period of 4 nm (L = 4 nm) and an effective mass of 0.5 (m²=0.5me), construct the Hamiltonian matrix at Gamma point (k = 0) by discretizing the 1D potential well to 10 points (N= 10). [10 points] b. Calculate the first four energy levels, i.e. smallest four eigenvalues of your Hamiltonian matrix in (a). (Matlab or Python are recommended for the computation but please feel free to use any programming language you know to solve the problem) [2 points] Consider a 1D finite potential well with a well width (a) of 2nm and a well depth (Vo) of 3 eV. E V₂ =3 ev a = 2 nm a. The infinite space can be approximated by periodic lattices. Assuming a period of 4 nm (L = 4 nm) and an effective mass of 0.5 (m²=0.5me), construct the Hamiltonian matrix at Gamma point (k = 0) by discretizing the 1D potential well to 10 points (N= 10). [10 points] b. Calculate the first four energy levels, i.e. smallest four eigenvalues of your Hamiltonian matrix in (a). (Matlab or Python are recommended for the computation but please feel free to use any programming language you know to solve the problem) [2 points]

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This problem involves creating a Hamiltonian matrix and calculating the energy levels of a 1D finite potential wellHeres how to solve it Part a Discretize the potential Divide the potential well into ... View the full answer